The stat really speaks for itself. How many points does a player score for every one of his missed shots? Really, it’s determining if a player brings more to the table than he takes from it. Every missed shot is a blown possession for his team while every make is a converted one.

We discovered that Dirk had an outstanding single-game PPM of 16 in Game 1. For every one of his misses, the big fellow scored SIXTEEN points. Simply outstanding.

However, as we thought about the stat more, and took the insightful and analytical contributions of commenters into consideration, we realized a few things.

As one reader pointed out,

“Had Dirk missed one more shot, his PPM would be 12. Had he missed 3 more shots, still a respectable 12-18, his PPM would be 8. Since this stat uses division, the numbers cannot be compared linearly. For example, comparing PPMs of 16 and 12 is not the same comparison as PPMs of 6 and 2, even though the difference between each is 4.”

Another thing we realized was that all shots are not created equal. Should a missed free throw count just as much as a missed field goal? Should missed three pointers count as much or more as a missed two-pointer?

Eventually we came to some conclusions about how PPM could be greatly improved.

First of all, missed threes and twos should count the same. Both misses (unless your team gets an offensive rebound) end up costing your team a possession. That’s one more possession where your team could have scored, but didn’t because you failed to convert.

The other question was about free throws. If you miss the first attempt of a two-shot foul, you haven’t necessarily lost your team a possession. In fact, you still get the opportunity to get your team a point. Really, free throws could be thought of as half of a field goal…since you normally get two of them and each shot is worth half of a field goal.

However, sometimes you only get one free throw because you earned an and-one. Other times, you are fouled on a three point attempt and get three freebies. We decided to use John Hollinger’s formula from his advanced statistic True Shooting Percentage to work out the details. He figured out a free throw attempt is worth 0.44 possessions.

That leads us to our final formula for figuring out Points Per Miss, which is slightly different from yesterday but more precise and useful:

PPM = Points / (Field Goals Missed + (0.44 x Free Throws Missed))

Because Dirk didn’t miss a single free throw, his PPM would still have been an outstanding 16. If he had missed one free throw, it would have dropped to 13.95. If he had missed one more field goal, it would have dropped to 12.
Obviously, with such an outstanding game, the results are likely to change A LOT with just one more make or miss.

However, the benefits of PPM are much more relevant when looking at someone’s season or career as a whole.

We will get to that in a second, but first I’ll address what I’m sure some of you are thinking: Wow…these guys have done nothing significant…this is just a ripoff of Hollinger’s True Shooting Percentage.

Let’s compare the two and discuss a few main points.

PPM = Points / (Field Goals Missed + (0.44 x Free Throws Missed))

True Shooting Percentage = Points / (2 x (FGA + (0.44 x FTA)))

The stats are very similar to say the least.

HOWEVER…

I believe they are different enough to both be useful, even together.

Percentage vs. Points

For one thing, Hollinger’s TSP gives you a percentage that the player shot from the floor. For instance, Dirk had a 61.2% True Shooting Percentage this year and Paul Pierce had a 62% True Shooting Percentage. With that stat, you get an idea of how well the guy shot from everywhere.

Our stat gives you an idea of how many points that guy scored for every miss. Dirk scored 2.85 points per miss and Pierce scored 2.79.

That difference is small, but it does give you a different sort of figure to compare the two players.

A More Complete Picture

The BIGGER difference I think is that it tells a more complete picture.

Let’s compare those two guys again. If you just looked at TSP, you would assume that Pierce is the more efficient scorer than Dirk, but if you really look at the stats that doesn’t make any sense.

Pierce averaged 18.9 points, shot 86% from the line, 37% from three, and 50% on all Field Goals.

Dirk averaged 23 points, shot 89% from the line, 39% from three, and 52% on all Field Goals.

So you have a guy who averaged MORE points and shot a better percentage from ALL THREE areas, but somehow he has a WORSE True Shooting Percentage than the other guy. That’s because True Shooting Percentage rewards players that score a higher percentage of their points from the free throw line. Dirk only scored 23% of his points from the foul line whereas Pierce scored 25% of his points from there this season.

Here is a more clear example.

Let’s pretend that two players both scored 30 points on a given night.

Player A was 10-20 from the floor and also finished 10-12 from the charity stripe. He missed 12 shots, and ended up with a PPM of 2.757. However, his True Shooting Percentage was 59%.

Player B was 14-24 from the floor, but only 2-4 from the foul line. He also missed 12 shots, and his PPM remains the same – 2.757. However, HIS True Shooting Percentage dips slightly to 58%.

Just by looking at TSP, the common person would believe that Player A was more efficient. However, that’s not really the case because while Player B did not shoot as well from the foul line, he actually shot BETTER from the field, which actually saved his team more possessions. Both players were equally effective. PPM shows that, TSP doesn’t.

All of that to say this:

I believe that our stat provides a more accurate picture of true efficiency on the offensive end of the floor than True Shooting Percentage.

It shouldn’t really matter where a player is getting his points. Some players score by getting to the free throw line. Other players score remarkably well without getting to the line. We need a stat that measures overall effectiveness correctly, and I believe that PPM helps us to accomplish that goal a little better.

At the end of the day, Dirk and Pierce are both remarkably efficient, and both deserve lots of credit for that. Like Jerod said yesterday, I had no idea Pierce was so efficient, and he now gets a lot more respect from me. But PPM provides a little more accurate picture of true efficiency.

When I look for efficiency, I am really looking for how many points per possession/shot/miss someone averaged. Percentages may lie; PPM doesn’t.

Below is a quick look at the top fifty scorers from the NBA this season, plus Steve Nash…because I’m always interested to see where he finishes in these types of stats.

What you will notice is that the PPM tends to lean a little more towards a) big men who get their shots around the basket and b) lights out shooters. This doesn’t really tell us anything new though, does it? Big men and great shooters are more efficient scorers than slashers and athletes.

A few interesting players of note: Derrick Rose, Kobe Bryant, and Russell Westbrook all fall out of the top ten and into the mid-30s. Meanwhile, Pau Gasol takes an almost meteoric rise up to #4.

Another player who is not on the list is Chris Paul. He ended up with a 2.444 PPM, putting him higher than all point guards not named Steve Nash and Tony Parker. However, his playoff PPM of 3.35 was unbelievable. Anyone who watched him against the Lakers would have said he was remarkably efficient…but good grief!

You can go up and down the list and make your own conclusions. It is fun and, in many cases, quite surprising.

FGM

FGA

FTM

FTA

Total Points

Missed FGA

Missed FTA

PPM

Dwight Howard

619

1044

546

916

1784

425

370

3.03504593399115

Dirk Nowitzki

610

1179

395

443

1681

569

48

2.84857317155833

Paul Pierce

507

1021

386

449

1511

514

63

2.78926382633095

Pau Gasol

593

1120

354

430

1541

527

76

2.74962529441153

Lebron James

758

1485

503

663

2111

727

160

2.64735390017557

Paul Millsap

525

988

256

338

1315

463

82

2.6348481205418

Steve Nash

399

811

227

249

1106

412

22

2.62284196547145

Ray Allen

480

978

193

219

1321

498

26

2.59304334170854

Chauncey Billups

339

794

384

419

1208

455

35

2.56802721088435

Kevin Love

482

1026

424

499

1476

544

75

2.5580589254766

Dwyane Wade

692

1384

494

652

1941

692

158

2.54884966908289

Chris Bosh

524

1056

384

471

1438

532

87

2.5215683523883

Kevin Martin

553

1267

594

669

1876

714

75

2.51137884872825

Tony Parker

555

1069

233

303

1368

514

70

2.51101321585903

Kevin Durant

711

1538

594

675

2161

827

81

2.50510062134842

Amar’e Stoudemire

744

1482

473

597

1971

738

124

2.4868779650752

Stephen Curry

505

1053

212

227

1373

548

15

2.47565813198702

David West

528

1040

264

327

1322

512

63

2.44941821685318

Zach Randolph

598

1188

300

396

1504

590

96

2.37884347716057

David Lee

496

978

210

267

1203

482

57

2.372406720833

LaMarcus Aldridge

707

1415

351

444

1769

708

93

2.36206804465096

Brook Lopez

644

1309

385

489

1673

665

104

2.35381844785863

Blake Griffin

696

1376

446

695

1845

680

249

2.33674451593292

Manu Ginobili

441

1018

357

410

1393

577

53

2.32042910447761

Wesley Matthews

440

979

266

315

1300

539

49

2.31910946196661

Carlos Boozer

431

845

171

244

1033

414

73

2.31552048776114

Carmelo Anthony

684

1503

507

605

1970

819

98

2.28506472416833

Luis Scola

569

1129

214

290

1352

560

76

2.2782421137773

Deron Williams

428

975

348

412

1309

547

64

2.27588844843174

Eric Gordon

427

949

287

348

1247

522

61

2.27206471831499

Rudy Gay

409

869

194

241

1069

460

47

2.22393276192061

Kobe Bryant

740

1639

483

583

2078

899

100

2.20360551431601

Derrick Rose

711

1597

476

555

2026

886

79

2.20035622746427

Al Jefferson

654

1319

220

289

1528

665

69

2.1974229176254

Josh Smith

497

1041

229

316

1274

544

87

2.18795081404135

Russell Westbrook

614

1390

531

631

1793

776

100

2.18658536585366

DeMar DeRozan

539

1154

327

402

1410

615

75

2.17592592592593

Luol Deng

531

1155

253

336

1430

624

83

2.16496093986556

Danny Granger

535

1260

395

466

1622

725

71

2.14482174970909

Andrea Bargnani

525

1173

287

350

1414

648

63

2.09258272657314

Monta Ellis

726

1611

340

431

1929

885

91

2.08531522961169

Nick Young

412

935

186

228

1115

523

42

2.05917116052301

Dorell Wright

485

1146

180

228

1344

661

48

1.97032780155984

Joe Johnson

514

1161

195

243

1312

647

48

1.96371909237861

Michael Beasley

561

1246

219

291

1401

685

72

1.95484735167718

Andray Blatche

426

957

220

283

1076

531

63

1.9258304696449

Stephen Jackson

435

1059

249

305

1240

624

56

1.91169215589541

Antawn Jamison

374

876

171

234

1010

502

63

1.90666767348788

John Wall

398

972

301

393

1131

574

92

1.84058065356073

Tyreke Evans

382

933

205

266

1012

551

61

1.75134985463104

Brandon Jennings

361

926

199

246

1019

565

47

1.73985794290398

Three more things of note.

First of all, no stat is perfect. The danger with all new stats is that we think we have figured out something so good that we no longer need to watch the game to decide how good a player is or is not. No one should look at this stat and decide that Derrick Rose, Kobe Bryant, and Russell Westbrook are bad players. However, it’s not surprising to anyone to see that they really aren’t super efficient on offense.

That’s the thing I love the most about this stat. In my opinion, it really reflects what you see. It’s more of a tangible verification than a new breakthrough. Anyone who has watched the Lakers all year would tell you that Pau is a more efficient scorer than Kobe, but even I didn’t think the difference would be that diverse.

Secondly, I think this stat is still a work in progress as far as what we can learn from it.

I have not had time to find out the league average for PPM yet, but it would be nice to figure that value out so we can really compare players. For instance, if you didn’t know anything about baseball, you would think that someone being successful at the plate only 30% of the time was awful. It isn’t until you realize what everyone is hitting that you understand that hitting .300 is fantastic.

With that said, PPM is still easy to understand because Points Per Miss is about as simplistic as it gets. Everyone who has ever watched basketball can understand that scoring 2.5 points per miss would be outstanding.

The other place this stat could really go is in terms of teamwork. I would be very interested to see how much a player’s presence on the floor affects his teammates’ PPM. Obviously LeBron James made his Cavs teammates more efficient players, but how much so? I believe this could be the next step of PPM.

Finally, I thought this comparison was telling: Reggie Miller’s career PPM was 2.632. Ray Allen’s is a paultry 2.304.

Jon Washburn grew up in Indianapolis, IN and as such, is a diehard Pacers, Colts, and Cubs fans. When it comes to college, he cheers for Notre Dame football fan and Purdue basketball. Yes, this sounds shady, but since he grew up without cable, he learned to love Notre Dame - the only team on TV. Glenn "The Big Dog" Robinson was at Purdue when Jon was in his formative years, so he latched onto them as well. Did that make him a fair-weather fan at the time? Sure. Give him a break...he was 8...and he has stayed with those teams ever since. Currently, he lives in Charleston, SC with his wife who grew up in Cleveland. Although he is no longer physically in the Midwest, his heart will always be there. Jon goes by the name "Twitch" because he has Tourette's Syndrome. Hit him up on his twitter @jwtwitch.

I think this could further be extended (or perhaps a different statistic) by adding in assists somehow. A player's aid to his teams score is 'points scored'+"points scored after an assist by this player". Now that I reread that, this would be a modification or extension of PPG… let's call it PPP or Points Per Player. Now, how would you figure that number into the others?

Why doesn't the metric take into account whether the FGA was a 2 or 3? While taking a 3 gives you more points, it also is (generally) riskier, so shouldn't you be punished more for missing a bunch of threes, rather an a bunch of twos? It's certainly debatable.

Shooting a 2 inherently increases reward due to the ability to draw more fouls and thus shoot more free throws. Which also makes me believe shooting 50% from inside the arc is not the same as shooting 33% from outside due to the assumed increase in free throw attempts.

Any idea as to how to quantify the benefit of shooting 2's? A simple formula would be FTA/(FGA-3PA), but that excludes the rare foul on a 3 point attempt and is probably missing something else. Also, what would the 3P% need to be when taking into account the opportunity cost of missed free throws? (I think 82games.com calculated what it needs to be at some point, but I can't remember what it ways)

The metric DOES take into account 2's versus 3's because your overall POINTS are affected by 2's and 3's.
For instance, let's say 2 guys both go 7 for 8. One guy makes 7 threes, and the other guy makes all twos. Player one would have a PPM of 21 and player 2 would only have a PPM of 14.
You don't really need to make a special formula for them because they are already affecting the PPM dramatically.

Just a thought on another potential method of weighing different types of shots/misses…

Rather than thinking about a missed shot as a loss of possession, one could view it as a loss of potential/expected points. A free throw may be worth .44 possessions, but it's a also point that most players in the league should be able to get. We can find the "expected" number of points for each type of shot by looking at league wide 3 point, 2 point, and free throw percentages. I don't have time right now to find the exact numbers for this, but using the medians as a point of reference, I found the following:

Not quite as pretty, but I think taking into account both the relative difficulty of the shots and their different values is an interesting idea. One can also think of WPPM as the ratio of the points a player scores to the points he was unable to score.

Also, his is kind of unrelated, but it just came to mind while writing this – it might even be interesting to use a completely different statistic, also assessing a player's efficiency by looking at a breakdown of his shot selection, measuring the percentage of "expected" points a player was able to score:

Obviously it's not perfect (especially since my league wide percentages aren't even correct), and maybe this has been done before, but I think it's a really interesting way of looking at efficiency, similar to what you've done here. It also has a very intuitive and understandable meaning. I'd like to see a few more players, but you mention with PPM, this confirms what we thought we've seen all season – Dirk is very efficient, Lebron is pretty efficient, and Rose struggles a bit with his efficiency.

You make the point in your example that player B "…shot BETTER from the field, which actually saved his team more possessions", however I don't think that is the case. Assuming both players only shot 2pt field goals and there were no "and-1's", both used 26 possessions and missed 10 FGs, leading to 10 loose ball opportunities. Both players A & B also missed 2 shots from the charity stripe. A miss on the 1st FT has no affect on the possession, but a miss on the 2nd leads to a loose ball, whereas a made shot simply hand the ball over to the opposing team. Of course the player should always try to make the FT, but if they're going to miss one, it would be more beneficial for them to miss the 2nd shot. If we assume the FT rebound goes to the opposite team, players A & B saved their teams the same number of possessions.

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Apple currently has Rhapsody as an app, which is a Terrific commence, nonetheless it is currently hampered through the incapacity towards retail store regionally on your iPod, and contains a dismal 64kbps little bit value. If this adjustments, then it will fairly negate this advantage for the Zune, nonetheless the Ten music for each thirty day period will continue to be a large moreover within just Zune Pass’ like.

Palms down, Apple’s app retailer wins as a result of a mile. It really is a massive preference of all types of programs vs a really disappointed choice of a handful for Zune. Microsoft includes systems, specifically within the realm of game titles, nevertheless I’m not sure I would need to have toward bet upon the long run if this element is major in direction of oneself. The iPod is a significantly better option within just that situation.

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Apple by now incorporates Rhapsody as an application, which is a best get started, nonetheless it is currently hampered by the lack of ability in direction of retail outlet locally on your iPod, and incorporates a dismal 64kbps little bit cost. If this alterations, then it will somewhat negate this advantage for the Zune, however the 10 music per thirty day period will however be a huge as well as inside of Zune Pass’ desire.

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Palms down, Apple’s application retail store wins by way of a mile. It is a massive quantity of all kinds of applications vs a pretty unsatisfied choice of a handful for Zune. Microsoft contains Designs, especially in the realm of game titles, but I am not guaranteed I’d require to bet on the long term if this component is essential to yourself. The iPod is a considerably superior decision in that situation.

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The Zune concentrates on currently being a Transportable Media Player. Not a web browser. Not a match machine. Probably within the foreseeable future it’s going to do even superior in those areas, but for currently it’s a exceptional direction in direction of organize and hear toward your music and flicks, and is without having peer in just that respect. The iPod’s advantages are its website viewing and apps. If people stable extra persuasive, maybe it is your least difficult selection.

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This is getting to be a little bit excess subjective, still I considerably favor the Zune Current market. The interface is colorful, is made up of more flair, and some amazing capabilities including ‘Mixview’ that permit you out of the blue perspective related albums, audio, or other customers equivalent in direction of what you’re listening to. Clicking on a person of those will center upon that solution, and a further preset of “neighbors” will occur into look at, enabling you to navigate close to researching by way of identical artists, music, or buyers. Talking of users, the Zune “Social” is in addition Wonderful enjoyment, letting on your own find other people with shared preferences and getting close friends with them. You then can listen toward a playlist crafted based on an amalgamation of what all your friends are listening to, which is furthermore thrilling. These worried with privateness will be relieved toward realize oneself can keep away from the community from looking at your person listening practices if yourself therefore just take.

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Among me and my husband we’ve owned even further MP3 gamers about the many years than I can count, including Sansas, iRivers, iPods (classic & touch), the Ibiza Rhapsody, etcetera. But, the closing few decades I’ve resolved down toward one line of avid gamers. Why? Considering the fact that I was happy in the direction of examine how well-designed and entertaining in the direction of employ the underappreciated (and extensively mocked) Zunes are.

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